Graph forms
for C4 [ 275, 5 ] = PS(5,55;16)
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On this page are computer-accessible forms for the graph C4[ 275, 5 ] =
PS(5,55;16).
(I) Following is a form readable by MAGMA:
g:=Graph<275|{ {55, 56}, {96, 112}, {97, 113}, {98, 114}, {99, 115}, {100, 116},
{101, 117}, {102, 118}, {103, 119}, {104, 120}, {105, 121}, {106, 122}, {107,
123}, {108, 124}, {109, 125}, {110, 126}, {160, 179}, {164, 183}, {161, 180},
{163, 182}, {162, 181}, {196, 222}, {197, 223}, {165, 184}, {192, 221}, {194,
223}, {195, 221}, {193, 222}, {195, 224}, {219, 248}, {215, 244}, {211, 240},
{199, 228}, {203, 232}, {207, 236}, {130, 166}, {131, 167}, {136, 172}, {137,
173}, {138, 174}, {139, 175}, {144, 180}, {145, 181}, {146, 182}, {147, 183},
{152, 188}, {153, 189}, {154, 190}, {155, 191}, {196, 225}, {220, 249}, {214,
243}, {212, 241}, {198, 227}, {204, 233}, {206, 235}, {198, 224}, {215, 241},
{214, 240}, {199, 225}, {206, 232}, {207, 233}, {72, 111}, {213, 242}, {88,
127}, {80, 119}, {197, 226}, {205, 234}, {81, 120}, {87, 126}, {85, 124}, {83,
122}, {200, 226}, {220, 246}, {217, 243}, {216, 242}, {201, 227}, {204, 230},
{205, 231}, {82, 121}, {86, 125}, {132, 168}, {133, 169}, {134, 170}, {135,
171}, {148, 184}, {149, 185}, {150, 186}, {151, 187}, {157, 176}, {218, 247},
{216, 245}, {159, 178}, {200, 229}, {202, 231}, {202, 228}, {219, 245}, {218,
244}, {203, 229}, {84, 123}, {217, 246}, {158, 177}, {201, 230}, {95, 111},
{148, 167}, {152, 171}, {156, 175}, {147, 166}, {153, 172}, {155, 174}, {8, 62},
{9, 63}, {154, 173}, {1, 57}, {2, 58}, {3, 59}, {4, 60}, {5, 61}, {6, 62}, {7,
63}, {73, 112}, {79, 118}, {77, 116}, {75, 114}, {2, 56}, {213, 239}, {212,
238}, {3, 57}, {6, 60}, {7, 61}, {208, 234}, {209, 235}, {74, 113}, {78, 117},
{140, 176}, {141, 177}, {142, 178}, {143, 179}, {149, 168}, {151, 170}, {208,
237}, {210, 239}, {4, 58}, {211, 237}, {5, 59}, {210, 236}, {76, 115}, {150,
169}, {209, 238}, {56, 127}, {8, 64}, {47, 103}, {46, 102}, {45, 101}, {44,
100}, {43, 99}, {9, 65}, {10, 66}, {11, 67}, {12, 68}, {13, 69}, {14, 70}, {15,
71}, {24, 80}, {25, 81}, {26, 82}, {27, 83}, {28, 84}, {29, 85}, {30, 86}, {31,
87}, {40, 96}, {41, 97}, {42, 98}, {10, 64}, {47, 101}, {46, 100}, {11, 65},
{14, 68}, {15, 69}, {26, 80}, {27, 81}, {30, 84}, {31, 85}, {42, 96}, {43, 97},
{128, 202}, {129, 203}, {132, 206}, {133, 207}, {144, 218}, {145, 219}, {12,
66}, {45, 99}, {44, 98}, {13, 67}, {28, 82}, {29, 83}, {130, 204}, {131, 205},
{146, 220}, {166, 247}, {168, 249}, {170, 251}, {172, 253}, {174, 255}, {169,
250}, {173, 254}, {168, 252}, {169, 253}, {170, 254}, {171, 255}, {16, 70}, {49,
103}, {48, 102}, {17, 71}, {24, 78}, {25, 79}, {134, 208}, {135, 209}, {142,
216}, {143, 217}, {171, 252}, {16, 72}, {54, 110}, {53, 109}, {52, 108}, {51,
107}, {50, 106}, {49, 105}, {48, 104}, {17, 73}, {18, 74}, {19, 75}, {20, 76},
{21, 77}, {22, 78}, {23, 79}, {18, 72}, {55, 109}, {54, 108}, {51, 105}, {50,
104}, {19, 73}, {22, 76}, {23, 77}, {136, 210}, {137, 211}, {140, 214}, {141,
215}, {128, 219}, {156, 192}, {157, 193}, {158, 194}, {159, 195}, {166, 250},
{167, 251}, {129, 220}, {20, 74}, {53, 107}, {52, 106}, {21, 75}, {138, 212},
{139, 213}, {167, 248}, {160, 196}, {161, 197}, {162, 198}, {163, 199}, {164,
200}, {165, 201}, {1, 110}, {32, 86}, {33, 87}, {40, 94}, {41, 95}, {32, 88},
{33, 89}, {34, 90}, {35, 91}, {36, 92}, {37, 93}, {38, 94}, {39, 95}, {34, 88},
{35, 89}, {38, 92}, {39, 93}, {36, 90}, {37, 91}, {58, 152}, {63, 157}, {62,
156}, {59, 153}, {111, 202}, {117, 208}, {119, 210}, {125, 216}, {127, 218},
{60, 154}, {61, 155}, {118, 209}, {126, 217}, {120, 211}, {124, 215}, {121,
212}, {123, 214}, {56, 150}, {57, 151}, {122, 213}, {118, 192}, {119, 193},
{126, 200}, {127, 201}, {57, 128}, {63, 134}, {61, 132}, {59, 130}, {120, 194},
{121, 195}, {124, 198}, {125, 199}, {58, 129}, {62, 133}, {112, 203}, {116,
207}, {113, 204}, {115, 206}, {122, 196}, {123, 197}, {60, 131}, {114, 205},
{35, 224}, {55, 244}, {51, 240}, {47, 236}, {43, 232}, {39, 228}, {25, 221},
{51, 247}, {50, 246}, {49, 245}, {48, 244}, {43, 239}, {26, 222}, {27, 223},
{32, 228}, {33, 229}, {34, 230}, {35, 231}, {40, 236}, {41, 237}, {42, 238},
{36, 225}, {54, 243}, {52, 241}, {46, 235}, {44, 233}, {38, 227}, {37, 226},
{88, 159}, {80, 151}, {72, 143}, {64, 135}, {53, 242}, {45, 234}, {65, 136},
{87, 158}, {85, 156}, {83, 154}, {81, 152}, {71, 142}, {69, 140}, {67, 138},
{112, 186}, {113, 187}, {116, 190}, {117, 191}, {66, 137}, {86, 157}, {82, 153},
{70, 141}, {36, 232}, {55, 251}, {54, 250}, {53, 249}, {52, 248}, {37, 233},
{38, 234}, {39, 235}, {40, 229}, {42, 231}, {114, 188}, {115, 189}, {41, 230},
{84, 155}, {68, 139}, {111, 185}, {73, 144}, {93, 132}, {91, 130}, {89, 128},
{79, 150}, {77, 148}, {75, 146}, {95, 134}, {74, 145}, {90, 129}, {78, 149},
{94, 133}, {44, 240}, {47, 243}, {46, 242}, {45, 241}, {48, 237}, {50, 239},
{64, 158}, {65, 159}, {49, 238}, {92, 131}, {76, 147}, {66, 160}, {71, 165},
{70, 164}, {67, 161}, {68, 162}, {69, 163}, {96, 135}, {104, 143}, {97, 136},
{99, 138}, {101, 140}, {103, 142}, {98, 137}, {102, 141}, {100, 139}, {1, 245},
{2, 246}, {3, 247}, {8, 252}, {9, 253}, {10, 254}, {11, 255}, {89, 160}, {91,
162}, {93, 164}, {105, 144}, {107, 146}, {109, 148}, {4, 255}, {90, 161}, {94,
165}, {106, 145}, {110, 149}, {4, 248}, {5, 249}, {6, 250}, {7, 251}, {28, 224},
{29, 225}, {30, 226}, {31, 227}, {1, 252}, {3, 254}, {32, 221}, {34, 223}, {2,
253}, {92, 163}, {33, 222}, {108, 147}, {5, 256}, {7, 258}, {13, 264}, {15,
266}, {21, 272}, {23, 274}, {6, 257}, {14, 265}, {22, 273}, {8, 259}, {12, 263},
{24, 275}, {12, 256}, {13, 257}, {14, 258}, {15, 259}, {28, 272}, {29, 273},
{30, 274}, {31, 275}, {9, 260}, {11, 262}, {10, 261}, {16, 260}, {17, 261}, {18,
262}, {19, 263}, {24, 268}, {25, 269}, {26, 270}, {27, 271}, {16, 267}, {20,
271}, {20, 264}, {21, 265}, {22, 266}, {23, 267}, {17, 268}, {19, 270}, {18,
269}, {172, 256}, {173, 257}, {174, 258}, {175, 259}, {188, 272}, {189, 273},
{190, 274}, {191, 275}, {175, 256}, {191, 272}, {176, 257}, {178, 259}, {180,
261}, {182, 263}, {184, 265}, {186, 267}, {188, 269}, {190, 271}, {177, 258},
{181, 262}, {185, 266}, {189, 270}, {176, 260}, {177, 261}, {178, 262}, {179,
263}, {184, 268}, {185, 269}, {186, 270}, {187, 271}, {179, 260}, {187, 268},
{180, 264}, {181, 265}, {182, 266}, {183, 267}, {183, 264}, {192, 273}, {194,
275}, {193, 274} }>;
(II) A more general form is to represent the graph as the orbit of {55, 56}
under the group generated by the following permutations:
a: (2, 55)(3, 54)(4, 53)(5, 52)(6, 51)(7, 50)(8, 49)(9, 48)(10, 47)(11, 46)(12,
45)(13, 44)(14, 43)(15, 42)(16, 41)(17, 40)(18, 39)(19, 38)(20, 37)(21, 36)(22,
35)(23, 34)(24, 33)(25, 32)(26, 31)(27, 30)(28, 29)(57, 110)(58, 109)(59,
108)(60, 107)(61, 106)(62, 105)(63, 104)(64, 103)(65, 102)(66, 101)(67, 100)(68,
99)(69, 98)(70, 97)(71, 96)(72, 95)(73, 94)(74, 93)(75, 92)(76, 91)(77, 90)(78,
89)(79, 88)(80, 87)(81, 86)(82, 85)(83, 84)(112, 165)(113, 164)(114, 163)(115,
162)(116, 161)(117, 160)(118, 159)(119, 158)(120, 157)(121, 156)(122, 155)(123,
154)(124, 153)(125, 152)(126, 151)(127, 150)(128, 149)(129, 148)(130, 147)(131,
146)(132, 145)(133, 144)(134, 143)(135, 142)(136, 141)(137, 140)(138, 139)(167,
220)(168, 219)(169, 218)(170, 217)(171, 216)(172, 215)(173, 214)(174, 213)(175,
212)(176, 211)(177, 210)(178, 209)(179, 208)(180, 207)(181, 206)(182, 205)(183,
204)(184, 203)(185, 202)(186, 201)(187, 200)(188, 199)(189, 198)(190, 197)(191,
196)(192, 195)(193, 194)(222, 275)(223, 274)(224, 273)(225, 272)(226, 271)(227,
270)(228, 269)(229, 268)(230, 267)(231, 266)(232, 265)(233, 264)(234, 263)(235,
262)(236, 261)(237, 260)(238, 259)(239, 258)(240, 257)(241, 256)(242, 255)(243,
254)(244, 253)(245, 252)(246, 251)(247, 250)(248, 249) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55)(56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110)(111, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165)(166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180,
181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196,
197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212,
213, 214, 215, 216, 217, 218, 219, 220)(221, 222, 223, 224, 225, 226, 227, 228,
229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244,
245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260,
261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275)
c: (1, 56, 111, 166, 221)(2, 72, 147, 192, 252)(3, 88, 128, 218, 228)(4, 104,
164, 189, 259)(5, 65, 145, 215, 235)(6, 81, 126, 186, 266)(7, 97, 162, 212,
242)(8, 58, 143, 183, 273)(9, 74, 124, 209, 249)(10, 90, 160, 180, 225)(11, 106,
141, 206, 256)(12, 67, 122, 177, 232)(13, 83, 158, 203, 263)(14, 99, 139, 174,
239)(15, 60, 120, 200, 270)(16, 76, 156, 171, 246)(17, 92, 137, 197, 222)(18,
108, 118, 168, 253)(19, 69, 154, 194, 229)(20, 85, 135, 220, 260)(21, 101, 116,
191, 236)(22, 62, 152, 217, 267)(23, 78, 133, 188, 243)(24, 94, 114, 214,
274)(25, 110, 150, 185, 250)(26, 71, 131, 211, 226)(27, 87, 112, 182, 257)(28,
103, 148, 208, 233)(29, 64, 129, 179, 264)(30, 80, 165, 205, 240)(31, 96, 146,
176, 271)(32, 57, 127, 202, 247)(33, 73, 163, 173, 223)(34, 89, 144, 199,
254)(35, 105, 125, 170, 230)(36, 66, 161, 196, 261)(37, 82, 142, 167, 237)(38,
98, 123, 193, 268)(39, 59, 159, 219, 244)(40, 75, 140, 190, 275)(41, 91, 121,
216, 251)(42, 107, 157, 187, 227)(43, 68, 138, 213, 258)(44, 84, 119, 184,
234)(45, 100, 155, 210, 265)(46, 61, 136, 181, 241)(47, 77, 117, 207, 272)(48,
93, 153, 178, 248)(49, 109, 134, 204, 224)(50, 70, 115, 175, 255)(51, 86, 151,
201, 231)(52, 102, 132, 172, 262)(53, 63, 113, 198, 238)(54, 79, 149, 169,
269)(55, 95, 130, 195, 245)
C4[ 275, 5 ]
275
-1 110 57 245 252
-2 253 56 58 246
-3 254 57 59 247
-4 255 58 60 248
-5 256 59 61 249
-6 257 60 62 250
-7 258 61 63 251
-8 259 62 64 252
-9 253 260 63 65
-10 66 254 261 64
-11 67 255 262 65
-12 66 68 256 263
-13 264 67 69 257
-14 265 68 70 258
-15 266 69 71 259
-16 267 70 72 260
-17 268 71 73 261
-18 269 72 74 262
-19 270 73 75 263
-20 264 271 74 76
-21 77 265 272 75
-22 78 266 273 76
-23 77 79 267 274
-24 275 78 80 268
-25 221 79 81 269
-26 222 80 82 270
-27 223 81 83 271
-28 224 82 84 272
-29 225 83 85 273
-30 226 84 86 274
-31 275 227 85 87
-32 88 221 228 86
-33 89 222 229 87
-34 88 90 223 230
-35 231 89 91 224
-36 232 90 92 225
-37 233 91 93 226
-38 234 92 94 227
-39 235 93 95 228
-40 236 94 96 229
-41 237 95 97 230
-42 231 238 96 98
-43 99 232 239 97
-44 100 233 240 98
-45 99 101 234 241
-46 242 100 102 235
-47 243 101 103 236
-48 244 102 104 237
-49 245 103 105 238
-50 246 104 106 239
-51 247 105 107 240
-52 248 106 108 241
-53 242 249 107 109
-54 110 243 250 108
-55 56 244 251 109
-56 55 2 127 150
-57 1 3 128 151
-58 2 4 129 152
-59 3 5 130 153
-60 154 4 6 131
-61 132 155 5 7
-62 133 156 6 8
-63 134 157 7 9
-64 135 158 8 10
-65 11 136 159 9
-66 12 137 160 10
-67 11 13 138 161
-68 12 14 139 162
-69 13 15 140 163
-70 14 16 141 164
-71 165 15 17 142
-72 143 111 16 18
-73 144 112 17 19
-74 145 113 18 20
-75 146 114 19 21
-76 22 147 115 20
-77 23 148 116 21
-78 22 24 149 117
-79 23 25 150 118
-80 24 26 151 119
-81 25 27 152 120
-82 121 26 28 153
-83 154 122 27 29
-84 155 123 28 30
-85 156 124 29 31
-86 157 125 30 32
-87 33 158 126 31
-88 34 159 127 32
-89 33 35 160 128
-90 34 36 161 129
-91 35 37 162 130
-92 36 38 163 131
-93 132 37 39 164
-94 165 133 38 40
-95 111 134 39 41
-96 112 135 40 42
-97 113 136 41 43
-98 44 114 137 42
-99 45 115 138 43
-100 44 46 116 139
-101 45 47 117 140
-102 46 48 118 141
-103 47 49 119 142
-104 143 48 50 120
-105 121 144 49 51
-106 122 145 50 52
-107 123 146 51 53
-108 124 147 52 54
-109 55 125 148 53
-110 1 126 149 54
-111 202 72 95 185
-112 203 73 96 186
-113 187 204 74 97
-114 188 205 75 98
-115 99 189 206 76
-116 77 100 190 207
-117 78 101 191 208
-118 209 79 102 192
-119 210 80 103 193
-120 211 81 104 194
-121 212 82 105 195
-122 213 83 106 196
-123 214 84 107 197
-124 198 215 85 108
-125 199 216 86 109
-126 110 200 217 87
-127 88 56 201 218
-128 89 57 202 219
-129 220 90 58 203
-130 166 91 59 204
-131 167 92 60 205
-132 168 93 61 206
-133 169 94 62 207
-134 170 95 63 208
-135 209 171 96 64
-136 210 172 97 65
-137 66 211 173 98
-138 99 67 212 174
-139 100 68 213 175
-140 176 101 69 214
-141 177 102 70 215
-142 178 103 71 216
-143 179 104 72 217
-144 180 105 73 218
-145 181 106 74 219
-146 220 182 107 75
-147 166 183 108 76
-148 77 167 184 109
-149 110 78 168 185
-150 56 79 169 186
-151 187 57 80 170
-152 188 58 81 171
-153 189 59 82 172
-154 190 60 83 173
-155 191 61 84 174
-156 192 62 85 175
-157 176 193 63 86
-158 177 194 64 87
-159 88 178 195 65
-160 66 89 179 196
-161 67 90 180 197
-162 198 68 91 181
-163 199 69 92 182
-164 200 70 93 183
-165 201 71 94 184
-166 147 247 250 130
-167 148 248 251 131
-168 132 149 249 252
-169 253 133 150 250
-170 254 134 151 251
-171 255 135 152 252
-172 253 256 136 153
-173 154 254 257 137
-174 155 255 258 138
-175 156 256 259 139
-176 157 257 260 140
-177 158 258 261 141
-178 159 259 262 142
-179 143 160 260 263
-180 264 144 161 261
-181 265 145 162 262
-182 266 146 163 263
-183 264 267 147 164
-184 165 265 268 148
-185 111 266 269 149
-186 112 267 270 150
-187 113 268 271 151
-188 114 269 272 152
-189 115 270 273 153
-190 154 116 271 274
-191 275 155 117 272
-192 221 156 118 273
-193 222 157 119 274
-194 275 223 158 120
-195 121 221 224 159
-196 122 222 225 160
-197 123 223 226 161
-198 124 224 227 162
-199 125 225 228 163
-200 126 226 229 164
-201 165 127 227 230
-202 231 111 128 228
-203 232 112 129 229
-204 233 113 130 230
-205 231 234 114 131
-206 132 232 235 115
-207 133 233 236 116
-208 134 234 237 117
-209 135 235 238 118
-210 136 236 239 119
-211 137 237 240 120
-212 121 138 238 241
-213 242 122 139 239
-214 243 123 140 240
-215 244 124 141 241
-216 242 245 125 142
-217 143 243 246 126
-218 144 244 247 127
-219 145 245 248 128
-220 146 246 249 129
-221 25 192 195 32
-222 33 26 193 196
-223 34 27 194 197
-224 198 35 28 195
-225 199 36 29 196
-226 200 37 30 197
-227 198 201 38 31
-228 199 202 39 32
-229 33 200 203 40
-230 34 201 204 41
-231 35 202 205 42
-232 36 203 206 43
-233 44 37 204 207
-234 45 38 205 208
-235 209 46 39 206
-236 210 47 40 207
-237 211 48 41 208
-238 209 212 49 42
-239 210 213 50 43
-240 44 211 214 51
-241 45 212 215 52
-242 46 213 216 53
-243 47 214 217 54
-244 55 48 215 218
-245 1 49 216 219
-246 220 2 50 217
-247 166 3 51 218
-248 167 4 52 219
-249 220 168 5 53
-250 166 169 6 54
-251 55 167 170 7
-252 1 168 171 8
-253 2 169 172 9
-254 3 170 173 10
-255 11 4 171 174
-256 12 5 172 175
-257 176 13 6 173
-258 177 14 7 174
-259 178 15 8 175
-260 176 179 16 9
-261 177 180 17 10
-262 11 178 181 18
-263 12 179 182 19
-264 13 180 183 20
-265 14 181 184 21
-266 22 15 182 185
-267 23 16 183 186
-268 187 24 17 184
-269 188 25 18 185
-270 189 26 19 186
-271 187 190 27 20
-272 188 191 28 21
-273 22 189 192 29
-274 23 190 193 30
-275 24 191 194 31
0